Can somebody explain how air war works? Manual does not give much details.

I am having some trouble understanding it. First of all I thought that having air superiority over hex should give you safe air strike possibility without much risk of intercept. On the other hand I thought that is also gives your unit safety against enemy air attacks. However that does not seem to be the case often.

When I am attacking with my "bombers" hex which is contested (yellow under air superiority filter) I get intercepted about 90% of the time. On the other hand I had situation when I was sitting in France (as Germany in 1944) with 4 "fighter" units level 3-4, air superiority filter was green over all of France yet I got my ground units constantly attacked with my fighters failing about 90% of time to intercept sustaining large looses to intercepting fighters (2-4 strength looses per enemy strike attack). I also noted that during AI turn air superiority filter over France turned red.

What should I do to get better chance of striking enemy ground units without being constantly intercepted (during French campaign I had 2 fighters against 1 French yet my bombers got intercepted most of the time when striking in to "yellow" hexes). And what should I do to protect my own units if placing 4 fighters around does not help?